how to draw 135 degree with a compass
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To construct 135 degree angle we first construct 90 degree angle and its steps of constructions are as follows:
1). Use ruler and draw a Line segment OB of any convenient length. (as shown below)

2). Now use compass and open it to any convenient radius. And with O as center , draw an arc which cuts line segment OB at X . (as shown below)

3). Again use compass and opened to the same radius (as of step 2). And with X as center , draw an arc which cuts first arc at D . (as shown below)

4). Again use compass and opened to the same radius (as of step 2). And with D as center , draw another arc which cuts first arc at C . (as shown below)

5). Again use compass and opened to the same radius (as of step 2). And With C & D as center, draw two arc which cuts each other at E . (as shown below)

6). Join OE and extent it to A. (as shown below)

7). Above formed angle AOB = 90 Degree .
8) . Extend BO to Z . (as shown below)

9). Since ZB is a straight line, so formed Angle AOZ = 90 Degree(angle sum property)

Now, to construct at 135 degree angle, we will construct the angle bisector of above angle AOB. And its done in the following steps:
10). Again use compass and open it to any convenient radius. And with O as center , draw an arc which cuts line segment OB at P and OA at Q . (as shown below)

11). Again use compass and opened to same radius (as of step 10).And with P & Q as center and, draw two arcs which cuts each other at point F. (as shown below)

12). Join OF and extend to E . (as shown below)

13). EO is the bisector of Angle AOB.
Therefore, Angle AOE = Angle EOB = ½ of Angle AOB = 45 Degree each (as shown below)

14). Now observe that:
Angle ZOA = 90�
Angle AOE = 45�
Add both the angles and we get
Angle ZOA + Angle AOE = 90� + 45� ���..(Statement 1)
Now observe the above diagram:
Angle ZOA + Angle AOE = Angle ZOE ��� (Statement 2)
From Statement 1 and 2, we get:
Angle ZOE = 135� (as highlighted with pink color)

1). Use ruler and draw a Line segment OB of any convenient length. (as shown below)

2). Now use compass and open it to any convenient radius. And with O as center , draw an arc which cuts line segment OB at X . (as shown below)

3). Again use compass and opened to the same radius (as of step 2). And with X as center , draw an arc which cuts first arc at D . (as shown below)

4). Again use compass and opened to the same radius (as of step 2). And with D as center , draw another arc which cuts first arc at C . (as shown below)

5). Again use compass and opened to the same radius (as of step 2). And With C & D as center, draw two arc which cuts each other at E . (as shown below)

6). Join OE and extent it to A. (as shown below)

7). Above formed angle AOB = 90 Degree .
8) . Extend BO to Z . (as shown below)

9). Since ZB is a straight line, so formed Angle AOZ = 90 Degree(angle sum property)

Now, to construct at 135 degree angle, we will construct the angle bisector of above angle AOB. And its done in the following steps:
10). Again use compass and open it to any convenient radius. And with O as center , draw an arc which cuts line segment OB at P and OA at Q . (as shown below)

11). Again use compass and opened to same radius (as of step 10).And with P & Q as center and, draw two arcs which cuts each other at point F. (as shown below)

12). Join OF and extend to E . (as shown below)

13). EO is the bisector of Angle AOB.
Therefore, Angle AOE = Angle EOB = ½ of Angle AOB = 45 Degree each (as shown below)

14). Now observe that:
Angle ZOA = 90�
Angle AOE = 45�
Add both the angles and we get
Angle ZOA + Angle AOE = 90� + 45� ���..(Statement 1)
Now observe the above diagram:
Angle ZOA + Angle AOE = Angle ZOE ��� (Statement 2)
From Statement 1 and 2, we get:
Angle ZOE = 135� (as highlighted with pink color)

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